In certain instances it is desirable to be able to reproduce many different patterns by printing before any one pattern is repeated. For example, in many states it is legal to play such games as bingo for the purpose of gambling. Generally, the prospective player purchases one or more bingo sheets, each of which will usually contain several bingo faces (five by five arrays), and then proceeds to play bingo in the usual manner simultaneously on each of the bingo faces. At the end of the game the bingo sheets are discarded after the winners have been determined and paid. Since a number of people may be playing bingo at the same time, it is highly desirable that each of the persons playing bingo have different sheets. Otherwise, more than one person would win at the same time using the identical bingo face. Accordingly, it is desirable to be able to print a large number of different bingo sheets, each having different bingo playing faces on them. In the past this problem has never been successfully solved.
According to John Scarne, Scarne's Guide to Casino Gambling, p. 313 (Simon and Schuster 1978), the number of bingo faces that could be printed is (24 numbers selected at random from 75 numbers):
111,007,923,832,370,565
but only about 9000 bingo faces are presently being used. These 9000 bingo faces represent a surface of 1000 square feet of printed paper. This is much larger than the surface area of a cylinder of a Webb press. Manufacturers of bingo sheets thus have to print the 9000 squares over 50 or more runs and then cut and assemble them like the pieces of a puzzle. Hence, today's manufacturers are in the position of the printer of a puzzle who has to separately print every piece of a multiplicity of puzzles, and then assemble them.
Moreover, the market is requesting larger and larger series. As bingo has become more popular, bingo games have included more than 1000 players, each one using 12 or 18 bingo faces simultaneously for 20 or 30 games. Five hundred thousand bingo faces can be used in one night by a single bingo operator. In some states, duplicate winners share the prize (winners resent it). In other states, the operator has to pay the full prize to every winner (the operator resents it). In both cases there is pressure on the manufacturers to increase the number of bingo faces without duplicates.
The use of a small (9000) series necessitates two precautions: (1) to print different color frames or outlines on each sheet to differentiate the sheets of one series from the sheets of the next series; up to 20 colors are used which necessitates an inventory of 20 times 50 runs; and (2) to print a serial number on every bingo face to identify bingo faces of the same series. Sheets from the same run are printed with different serial numbers This makes assembling the pieces of the puzzle even more difficult.
Previously, large runs have been made of identical bingo sheets within each run. Large numbers of such runs have been made with the sheets from each run having different bingo faces. Then, collation has been carried out to provide sets of non-identical bingo sheets with each set having a large number of different sheets. To be able to provide such sets of different sheets, the printers have had to maintain truly huge inventories. The problem is further exacerbated by the requirement that the sets be available in several (generally twelve) different color combinations so that sheets from one game cannot become confused during play with sheets from previous games.
While printing is, of course, a quite old art and a number of wet printing machines are known, none will solve the above described problem. For example, some of this art is described in U.S. Pat. No. 1,973,034, issued Sep. 11, 1934 to H. V. Ball, U.S. Pat. No. 3,015,266, issued Jan. 2, 1962 to C. U. Anderson et al., U.S. Pat. No. 3,621,780, issued Nov. 23, 1971 to J. S. Tillotson, and U.S. Pat. No. 3,083,640, issued Apr. 2, 1963 to C. Milner. Such printing machinery as is shown in the four just-mentioned patents is designed primarily for producing multicolor printing on various media.
U.S. Pat. No. 3,083,640 discloses a particularly interesting apparatus for irregularly dyeing yarn. Parallel strands of yarn are fed through an apparatus having a series of printing rolls having different effective radii and circumferences. It is required that the circumference of the largest roll and the circumference of at least one of the other rolls in the series be in fractional relationship as opposed to whole number relationship. In this manner, an irregularly dyed series of strands of yarn are prepared. As will be apparent, such an apparatus is not useful for printing bingo sheets or other patterns having a series of separate images which must be specifically positioned.
A security problem also exists with bingo sheets. Players have been known to attempt to cheat by altering the face of the card so that they have apparently won. For example, the number 3 is sometimes modified to look like the number 8 if the number 8 would lead to a win situation for the player. When there are only nine thousand bingo faces used before repitition, the persons or firm running the game can keep a book with the nine thousand bingo faces shown in it and can affix a serial number to each bingo sheet, for example a number from 1 to 9000, and then check each purported winder against the book. If larger numbers of non-repetitive bingo faces should become available, for example as taught hereinbelow, such a method would not be practical. For example, if one could produce one million bingo sheets without repitition, even if each such sheets bore a serial number from 1 to 999,999, one would need a book one million pages long to check each purported winning bingo face. As a practical matter such would be impossible.